Collets employed for use with Bridgeport-type milling machines have conventionally been made by drilling a uniform longitudinal bore through the rear and central portions of the collet, following which a bushing is inserted into the rear portion of the bore. The bushing has a threaded bore of reduced cross-sectional area for attachment to the milling machine. In the manufacture of this type of collet, production cost is increased since the assembly of the two parts of the collet is time-consuming. Additionally, it has been found that the two part assembly causes problems when used including, inter alia, the loosening of the bushing with use, difficulty in controlling optimum assembly procedures, and inability to maintain the concentricity of the bushing thread.